On Certain Numbers Associated to Isolated Critical Points.
On infinitesimal deformations of rational surface singularities
On polar invariants of hypersurface singularities
On Steenbrink's conjecture.
On the discriminant of the Artin component
On the genus of reducible surfaces and degenerations of surfaces
We deal with a reducible projective surface with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the -genus of , i.e. the dimension of the vector space of global sections of the dualizing sheaf . Then we prove that, when is smoothable, i.e. when is the central fibre of a flat family parametrized by a disc, with smooth general fibre, then the -genus of the fibres of is constant.
On the Module of Zariski Differentials and Infinitesimal Deformations of Cusp Singularities.
On the uniqueness of the quasihomogeneity
The aim of this paper is to show that the quasihomogeneity of a quasihomogeneous germ with an isolated singularity uniquely extends to the base of its analytic miniversal deformation.
On vanishing inflection points of plane curves
We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs which take into account the inflection points of the fibres of . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.
Résolution de Nash des points doubles rationnels
Nous présentons une méthode qui permet de calculer le transformée de Nash (et sa normalisation) d’une singularité de surface pour laquelle on dispose d’une résolution explicite. Comme exemple nous calculons la résolution des points doubles rationnels obtenue par itération du transformé de Nash normalisé.
Résolution simultanée de points doubles rationnels
Rolling factors deformations and extensions of canonical curves.
Simultaneous Resolution of Threefold Double Points.
Small Deformation of Normal Singularities (Erratum).
Small Deformations of Normal Singularities.
Smoothing of rational m-ropes
In a recent paper, Gallego, González and Purnaprajna showed that rational 3-ropes can be smoothed. We generalise their proof, and obtain smoothability of rational m-ropes for m ≥ 3.
Smoothings of cusp singularities via triangle singularities
Strata in the deformation of real isolated singularities are in general non contractible
Survey of recent results on singularities of equivariant maps
The concept of (ν)-equivalence in algebraic deformation theory